In simplest form, a radar system consists of the generation of a pulse having a certain duration, followed by a listening period in which returns are received. A radar designer usually wishes to increase the power of target returns to provide better detection. The most straightforward way to do this is to increase pulse amplitude. Unfortunately, useful radars require pulse amplitudes that would result in waveguide arcing and electrical breakdown. A conventional way to circumvent this problem is to use pulse compression techniques, i.e. transmitting a series of low amplitude pulses (subpulses) of the same aggregate energy as a higher amplitude pulse. The pulses are typically modulated (the modulated pulse also called a coded waveform) and transmitted. Returns are processed through a matched filter (i.e. a filter whose transfer function optimizes the signal to noise ratio), resulting in a signal that is a compressed pulse that is also the auto-correlation of the coded waveform in the absence of doppler shifts. Pulse coding can be expressed in matrix form, examples of which are matrices for the well-known Frank and P4 codes. The matrix describes the phase shifting necessary to phase modulate the subpulses of a coded pulse. This matrix is a square matrix of dimension N.times.N, each element of which represents a phase shift (the phase modulation) of one subpulse. The Frank or P4 code consists of concatenated N.sup.2 subpulses having the phases described by the elements of the consecutive rows of the matrix, reading from left to right. An example of a Frank matrix is shown in FIG. 1 for N=4. The elements of, e.g., the second row, 1, j, -1, -j, describe the fifth to eighth subpulses with respective phase modulation of 1 (i.e. 0.degree.), j (i.e. 90.degree.), -1 (i.e. 180.degree.) , and -j (i.e. -90.degree. ).
Such a radar system commonly operates by generating a sequence of identically coded waveforms, separated in time by detection, or listening intervals, in which the radar can detect returns of the transmitted waveform. The range for which the radar can receive unambiguously is limited to the distance a pulse can travel to and from the radar during its detection interval. This distance is called the unambiguous range. Often, downrange from the unambiguous range is clutter (e.g. hills) which can reflect radar returns, and such clutter can cause pulses to return to the radar during detection intervals for later pulses (i.e. be "folded over" into a later detection interval). Clutter causing foldover into the next pulse's detection interval is said to be located in the first ambiguous range, foldover into the second succeeding detection interval is said to be from the second ambiguous range, etc. Unambiguous range clutter is undesirable because it increases the cancellation requirements of the radar and the dwell time required to process clutter returns, and because it causes the range to be ambiguous in mapping applications.